I've been making my templates by just saving a psd file but that brings up the problem that I might save over the template on accident.
When I go to File> I don't see a "Save as Template" option. Is it somewhere else?
Photoshop has no inherent template format.
That being posted your operating system may have an option.
On the MacOS, you can choose File > Get Info on a file of practically any type, including .psd and tick the "Stationary Pad" option in the Finder. This will cause a copy of the file to open when chosen. Same basic operation as a template format.
I wouldn't know if this is possible on Windows. But surely it must be.